Platonic Solids

11 10 the cube 6 faces 12 edges 8 vertices The cube has octahedral symmetry below. Plato assigned it to the element of Earth due to the stability of its square bases. Aligned to our experience of space it faces forwards, backwards, right, left, up and down, corresponding to the six directions North, South, East, West, zenith and nadir. Six is the first perfect number, with factors adding up to itself 1 2 3 6. Add the cubes twelve edges, the twelve face diagonals and the four interior diagonals to find a total of twentyeight straight paths joining the cubes eight vertices to each other. Twentyeight is the second perfect number 1 2 4 7 14 28. Islams annual pilgrimage is to the Kaaba, literally Cube, in Mecca. The sanctuary of the Temple of Solomon was a cube, as is the crystalline New Jerusalem in Saint Johns revelation. In 430 BC the oracle at Delphi instructed the Athenians to double the volume of the cubic altar of Apollo, whilst maintaining its shape. Doubling the cube, as the problem became known, ultimately proved impossible using Euclidean geometry alone.